If R is a primitive ring with identity and e R is such that e 2 e 0, then (a) e R e is a subring of R, with identity e (b) e R e is primitive ...

a eRe is a subring of R with identity e Explanation Since R is a primitive ring with identity it means that R has no nontrivial twosided ideals ie ide ...

If R is a primitive ring with identity and e R is such that e 2

Question:

If R is a primitive ring with identity and e ϵ R is such that e² = e ≠ 0, then

(a) eRe is a subring of R, with identity e.

(b) eRe is primitive.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

See More Books

Question Posted: Aug 03, 2023 08:24 AM

See More Questions

Consider the figure. Draw a figure and give a similar proof for (a + b) 2 = a 2 + 2ab + b 2 . a b b
Every torsion-free divisible abelian group D is a direct sum of copies of the rationals Q. if O n e Z and D, then there exists a unique b D such that nb = a. Denote h by (1/n)a. For m, n Z (n ...
(a) Let S be a nonempty set and let N s be the set of all functions : S N such that (s) O for at most a finite number of elements s S. Then N s is a multiplicative abelian monoid with product...
Two thousand kg of water, initially a saturated liquid at 150C, is heated in a closed, rigid tank to a final state where the pressure is 2.5 MPa. Determine the final temperature, in C. the volume of...
Paul Scott Company reports net sales of $800,000, gross profit of $370,000, and net income of $240,000. What are its operating expenses?
Real Characteristic Roots: Determine the general solutions for the differential equations in Problems 1-3? 1. y" = 0 2. y" - y' = 0 3. y" - 9y = 0
Let us consider an activity, whose level is measured by a continuous decision variable . A concrete example would be the amount of an asset that we purchase. The cost of the activity may include both...
At the end of May, the first month of operations, the following selected data were taken from the financial statements of Julie Mortenson, Attorney at Law, P.C.: Net income for May ....... $127,500...
What was the biggest ethical violation of the Enron case and what lessons were learned? Is it true, that one of Enron's problems to date is poor corporate governance? As the senior executive officer,...
The following conditions on a semi simple module A are equivalent: (a) A is finitely generated. (b) A is a direct sum of a finite number of simple submodules. (c) A has a composition series. (d) A...
(a) The homomorphic image of a semi simple ring need not be semi simple. (b) If : R S is a ring epimorphism, then f(J(R}) J(S).
Describe how the cells of the acquired-immunity system develop so that they do not recognize self-antigens but do recognize foreign antigens.
The PDIC shall not pay deposit insurance insurance for the following accounts or transactions, except for: Deposit accounts which are unfunded, fictitious or fraudulent Deposit products constituting...
Celestila Moonn, a GLBAAF 310 student at UMB, just arrived in Tokyo, Japan. After completing the currency exchange from U.S dollar to yen, Moonn made the following statements: Statement 13: Before...
In the central bank's first public speech since increasing the cash rate 0.25 of a percentage point to 4.35 percent last week, the RBA's acting chief economist. Marion Kohler, said that the next...
Tyler Industries operates a mineral deposit with an estimated 1,500,000 tons of available ore. The mineral deposit was purchased for $1,500,000, and no salvage value is expected. A total of 200,000...
The third important part of a wave is its Wavelength, which is also measured in centimeters. What is the definition of wavelength?
Three fair coins are tossed. We wish to find the probability of the event A: {Observe at least one head.} a. Express A as the union of three mutually exclusive events. Using the expression you wrote,...
Danielle has an insurance policy with a premium of $75 per month. In September she is in an accident and receives a bill worth $2990 for the repair of her own property. Her deductible is $250 and her...
Perform the test in Problem 14.80, and report a p-value (two-tail)? Cancer A paper was recently published concerning the association between alcohol consumption and breast cancer incidence based on...
What test can be performed to compare the breast cancer incidence rate between the ¥ 30.0g group and the 0g group? Cancer A paper was recently published concerning the association between alcohol...
Interpret what the results mean. Specifically, did the screening program have a significant impact on breast cancer mortality or not? One issue is that there may be time trends in breast cancer...
12. A friend wishes to invest some money in one of three ordinary shares. For each company the mean and standard deviation of the annual percentage returns over the last 10 years are given below....
Stock X and the "market" had the following returns during the last three years, and the same relative volatility is expected to exist in the future: Stock X Market Year 15.0 10.0 1 5.0 -15.0 5.0 -5.0...
A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that...

If R is a primitive ring with identity and e R is such that e 2

Question:

Step by Step Answer:

a eRe is a subring of R with identity e Explanation Since R is a primitive ring with identity it means that R has no nontrivial twosided ideals ie ide...View the full answer

Algebra Graduate Texts In Mathematics 73

Students also viewed these Mathematics questions